Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.     

A study of the mode-selective trans--cis isomerization in HONO using ab initio methodology

Ab initio calculations on the six-dimensional cis--trans double minimum potential energy surface of the electronic ground state of the HONO molecule were performed using a coupled cluster approach. An analytic fit to the data points was established. The interconversion barrier was calculated to be 4105 cm(-1). The nuclear motion problem was solved variationally using a full six-dimensional Hamiltonian in internal coordinates. The eigenstates up to about 3650 cm(-1) were tentatively assigned by harmonic quantum numbers. The assignment was based on the mean values of the internal coordinates of the six-dimensional eigenfunctions and on a comparison of the eigenenergies with those calculated by second-order perturbation theory from a full quartic force field in dimensionless normal coordinates. In cold matrices the trans- and the cis-OH nu(1) stretching modes and the first trans- and cis-NO 2nu(2) stretching overtones lead to isomerization. In the isolated molecule these modes (J=0) were found to be entirely localized. However, several overtones of the nu(4) ONO bending and nu(5) N-O stretching, which are close in energy to the OH stretch and combined with the torsional mode, were found to be strongly cis-trans delocalized.     

Internal coordinate density of state from molecular dynamics simulation

The vibrational density of states (DoS), calculated from the Fourier transform of the velocity autocorrelation function, provides profound information regarding the structure and dynamic behavior of a system. However, it is often difficult to identify the exact vibrational mode associated with a specific frequency if the DoS is determined based on velocities in Cartesian coordinates. Here, the DoS is determined based on velocities in internal coordinates, calculated from Cartesian atomic velocities using a generalized Wilson's B ‐matrix. The DoS in internal coordinates allows for the correct detection of free dihedral rotations that may be mistaken as hindered rotation in Cartesian DoS. Furthermore, the pronounced enhancement of low frequency modes in Cartesian DoS for macromolecules should be attributed to the coupling of dihedral and angle motions. The internal DoS, thus deconvolutes the internal motions and provides fruitful insights to the dynamic behaviors of a system. © 2015 Wiley Periodicals, Inc.     

Partial optimization of large molecules and clusters

By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.     

Using internal coordinates to describe photoinduced geometry changes in MLCT excited states

A resonance Raman intensity analysis of the metal-to-ligand charge-transfer (MLCT) transition for the rhenium compound Re(2-(2'-pyridyl)quinoxaline)(CO)(3)Cl (RePQX) is presented. Photoinduced geometry changes are calculated, and the results are presented using the vibrational normal modes and the redundant internal coordinates. A density functional theory calculation is used to determine the ground-state nonresonant Raman spectrum and a transformation matrix that transforms the redundant internal coordinates into the normal modes. The normal modes nu(37) (rhenium coordination sphere distortion) and nu(75) (ligand skeletal stretch) show the largest photoinduced geometry change (Delta = 1.0 and 0.7, respectively). A single carbonyl mode is enhanced in the resonance Raman spectra. Time-dependent density functional theory is used to calculate excited-state geometry changes, which are subsequently used to determine the signs of the photoinduced normal mode displacements. Transforming to internal coordinates reveals that all the CO bond lengths are displaced in the excited state. The Re-C and C-C ligand bond lengths are also displaced in the excited state. The results are discussed in terms of a simple one-electron picture for the electronic transition. Many bond angles and torsional coordinates are also displaced by the metal-to-ligand charge transfer, and most of these are associated with the rhenium coordination sphere. It is demonstrated that using internal coordinates presents a clear picture of the geometry changes associated with photoinduced electron transfer in metal polypyridyl systems.     

Initial excited-state structural dynamics of 2'-deoxyguanosine determined via UV resonance Raman spectroscopy

The resonance Raman spectra of 2'-deoxyguanosine, a DNA nucleoside, were measured in aqueous solution at wavelengths throughout its 260 nm absorption band. Self-consistent analysis of the resulting resonance Raman excitation profiles and absorption spectrum using a time-dependent wave packet formalism with two electronic states yielded the initial excited-state structural dynamics in both states. The vibrational modes containing the N(7)═C(8) stretching and C(8)-H bending internal coordinates were found to exhibit significant initial structural dynamics upon photoexcitation to either state and are coincident with the photochemical reaction coordinate involving the formation of the 2'-deoxyguanosine cation radical.     

Force Constant Calculation in Mass-Weighted Cartesian Coordinates. Linear XYX and XYZ Type Molecules

Force constants of simple linear XYX and XYZ types of molecules have been calculated in using the method of mass-weighted cartesian coordinates. Relations and results between force constants in mass-weighted cartesian coordinates and in internal coordinates were also discussed.     

The phonon spectrum of phase-I ammonia: reassignment of lattice mode symmetries from combined molecular and lattice dynamics calculations

The zone-center phonon spectra of phase-I ammonia and deuterated ammonia have been obtained from plane-wave DFT molecular dynamics and localized basis set harmonic lattice dynamics simulations. These data have proved to be excellent for benchmarking the two approaches. Significant changes to the assignments of the experimental low-frequency lattice modes are proposed on the basis of the calculated data. The magnitude of the splitting of the longitudinal and transverse optical modes has been determined and is shown to be significant in some cases. The high-frequency internal mode region of the spectrum has also been obtained and is shown to be in excellent agreement with the results of previous studies. The symmetry coordinates and Davydov splittings of the internal modes are fully analyzed.     

Ab initio vibrational transition dipole moments and intensities of formaldehyde

Vibrational transition dipole moments and absorption band intensities for the ground state of formaldehyde, including the deuterated isotopic forms, are calculated. The analysis is based on ab initio SCF and CI potential energy and dipole moment surfaces. The formalism derives from second-order perturbation theory and involves the expansion of the dipole moment in terms of normal coordinates, as well as the incorporation of point group symmetry in the selection of the dipole moment components for the allowed transitions. Dipole moment expansion coefficients for the three molecule-fixed Cartesian coordinates of formaldehyde are calculated for internal and normal coordinate representations. Transition dipole moments and absorption band intensities of the fundamental, first overtone, combination, and second overtone transitions are reported. The calculated intensities and dipole moment derivatives are compared to experiment and discussed in the context of molecular orbital and bond polarization theory.     

Prediction of DNA far-IR absorption spectra based on normal mode analysis

 We present a computational method which couples normal mode analysis in internal coordinates of a molecule with very far IR spectroscopy. The analytical expression for the dependence of IR absorption on frequency incorporates frequencies and optical activities of each normal mode. In order to predict far-IR spectra of a molecule we evaluate the optical activity of each normal mode. This optical activity is determined by the vibration amplitude of the dipole moment produced by a normal mode. We calculated normal modes of DNA double-helical fragments (dA)₁₂ · (dT)₁₂ and (dA-dT)₆ · (dA-dT)₆ and evaluated their optical activities. These were found to be very sensitive to the DNA base-pair sequence. The positions of the resonance peaks in the calculated absorption spectrum of (dA)₁₂ · (dT)₁₂ are in a good agreement with those obtained by Fourier transform IR spectroscopy (Powell JW et al. 1987 Phys Rev A 35: 3929–3939). Received: 20 June 2000 / Accepted: 5 January 2001/ Published online: 3 May 2001     

Ab initio calculation of resonance Raman cross sections based on excited state geometry optimization

A method for the calculation of resonance Raman cross sections is presented on the basis of calculation of structural differences between optimized ground and excited state geometries using density functional theory. A vibrational frequency calculation of the molecule is employed to obtain normal coordinate displacements for the modes of vibration. The excited state displacement relative to the ground state can be calculated in the normal coordinate basis by means of a linear transformation from a Cartesian basis to a normal coordinate one. The displacements in normal coordinates are then scaled by root-mean-square displacement of zero point motion to calculate dimensionless displacements for use in the two-time-correlator formalism for the calculation of resonance Raman spectra at an arbitrary temperature. The method is valid for Franck-Condon active modes within the harmonic approximation. The method was validated by calculation of resonance Raman cross sections and absorption spectra for chlorine dioxide, nitrate ion, trans-stilbene, 1,3,5-cycloheptatriene, and the aromatic amino acids. This method permits significant gains in the efficiency of calculating resonance Raman cross sections from first principles and, consequently, permits extension to large systems (>50 atoms).     

Photoionization-induced dynamics of the ammonia cation studied by wave packet calculations using curvilinear coordinates

The determination of the photoelectron spectrum of NH₃ and of the internal conversion dynamics of recently published [A. Viel, W. Eisfeld, S. Neumann, W. Domcke, U. Manthe, J. Chem. Phys. 124 (2006) 214306] is complemented by the investigation of the effect of the vibrational angular momenta couplings on the dynamics. The multi-configurational time-dependent Hartree method is used to propagate a wave packet on the analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation. Curvilinear coordinates and the associated quasi-exact kinetic energy operator suitable for the multi-configurational time-dependent Hartree scheme are employed. A non-negligible effect of the use of Cartesian normal modes instead of the curvilinear coordinates is observed on the low energy part of the photoelectron spectrum. However, the three different time scales found in the dynamical calculations for the second absorption band are very similar regardless of the use of either normal modes or curvilinear coordinates.     

A theoretical anharmonic study of the infrared absorption spectra of FHF-, FDF-, OHF-, and ODF- anions

Anharmonic vibrational frequencies, equilibrium bond lengths, rotational constants, and vibrational absorption spectra have been calculated for the triatomic anions, FHF(-) and OHF(-), and the heavier isotopomers FDF(-) and ODF(-). The triatomic anions are assumed to maintain a collinear configuration throughout all calculations, so only the symmetric (nu(1)) and asymmetric (nu(3)) stretching modes are considered. The two-dimensional permanent dipole surfaces and potential energy surfaces are then constructed along bond coordinates, using high-level ab initio methods. Fundamental and combination bands are obtained from the vibrational eigenfunctions, resulting in anharmonic frequencies, which can be compared with the available theoretical and experimental data. The agreement is very good, especially for the pure symmetric modes, while the asymmetric ones show larger discrepancies, presumably due to the neglected coupling between stretching and bending modes. Strong inverse anharmonicity is found in the level spacing of the asymmetric modes, for both FHF(-) and OHF(-) anions. The calculated mixed modes (nnu(1)+mnu(3), n, m=0-3) also agree reasonably with the few available experimental data, supporting our model. Based on the vibrational eigenfunctions, isotope effects are also rationalized. Infrared absorption spectra are calculated from the dipole autocorrelation function for FHF(-) and FDF(-), and for OHF(-) and ODF(-). Peak locations and relative intensities are assigned in terms of the fundamental and mixed transitions.     

Calculation of the O-H stretching vibrational overtone spectrum of the water dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.     

On the effect of molecular structure on the superposition of normal modes of vibration

The normal modes of vibration in cartesian coordinates were calculated for ethylene, C₂H₄, and an ethylene complex, C₂H₄-Tl³⁺-H₂O, which is presumably formed during the catalytic oxidation of C₂H₄. For the CC bond of C₂H₄ as the critical coordinate of this reaction the distortions were then calculated which are caused by superimposing the normal modes. These calculations indicate that the maximum distortion of the CC bond which is attainable by superimposing normal modes in their ground state is larger in some conformations of the complex than in the free molecule. This indicates the general possibility that, depending on proper symmetry, complex formation may increase the reactivity of a compound because, compared to the free molecule, the superposition of a greater number of 3N-6 normal modes can produce greater momentary distortions of internal coordinates. The effect could be of considerable importance for the reactivity of very large systems, like, e.g., enzyme-substrate complexes.     

Vibrational spectra and conformational isomerism of calixarene building blocks. III. 2,6-Dimethylanisole and n-propyl-2,6-dimethylphenyl ether

The conformations and vibrational spectra of the 2,6-dimethylanisole and n-propyl-2,6-dimethylphenyl ether molecules have been analysed within the framework of density functional theory. The calculated force field (B3LYP/6-31G^*) has been transformed to internal coordinates, and the set of 10 different scaling factors has been applied. The scaled quantum mechanical method reproduces the experimental range of the IR and Raman spectra with high accuracy. According to the computations, the conformational behaviour of the alkyl aryl ethers studied is similar to the related dialkyl ether molecules, i.e. the CO–CC bond prefers the anti conformation, while the OC–CC bond prefers the gauche conformation. The major part of the vibrational spectra of the title compounds can be approximated by the sum of the vibrational modes of their constituent groups, these modes being transferable among the related molecules.     

Quantum chemistry study on internal conversion of diphenyldibenzofulvene in solid phase

We investigate the nonradiative decay process of diphenyldibenzofulvene (DPDBF) in solid phase by using the quantum chemistry methods. To carry out the nonradiative rate constant calculation, we construct a solid phase model based on the ONIOM method. The geometry of the DPDBF molecule is optimized for the ground state by DFT and the first excited state by TD-DFT, and the corresponding vibrational frequencies and normal coordinates are computed. Under displaced-distorted harmonic oscillator potential approximation, Huang-Rhys factors are obtained. Vibronic coupling constants are calculated as a function of the normal mode based on Domcke's scheme. We find that vibronic coupling constants of 12 modes with large reorganization energies are of similar order, and if this result is still valid for other modes, the internal conversion rate would be determined by high frequency modes because they have a significant nuclear factor that is related to Franck-Condon overlap intergrals. We also find that geometrical changes are suppressed due to the stacking effect, which yields small Huang-Rhys values in the solid phase.     

An ab initio calculation of symmetric bending and stretching vibrational states of the H3O+ and D3O+ ions

Calculations are reported for the symmetric bending and stretching vibrational states of H₃O⁺ and D₃O⁺ including coupling between these two modes. The calculations were carried out by using a potential surface calculated by the SCF CI method and expressed in terms of symmetric internal coordinates. The transition energy of the ν₂ (1^? ← 0⁺) inversion mode is found to be 985 cm^?1, which is comparable to the experimental value of 954.417 cm^?1 observed by Haese and Oka. The calculated inversion doubling of the lowest state is 51 cm^?1.